The liquid$-$phase reactionA $+$ B Cfollows an elementary rate law and is carried out isothermally in a $200$ L batch reactor that can be heated to $77\backslash$deg C or cooled to $0\backslash$deg C$.$ The initial concentrations of A and B are $1$ mol$/$L$.$ At $300$ K$,$ k $=0\mathrm{.}07$ L$/$mol$$min and E $=20$ kcal$/$mol$.$ How long would it take to achieve $90\%$ conversion at $77\backslash$deg C and at $0\backslash$deg C$?$